Colocalizations and their realizations as spectra

Friedrich W. Bauer

Every chain functor $A_*$, admits a $L$-colocalization
$A^L_*$ which (in contrast to the case of
$L$-localizations) in general does not allow a
realization as a spectrum (even if $A_*$ stems from a spectrum
itself). The $[E, ]_*$- colocalization of A. K. Bousfield is
retrieved as a special case of a general colocalization process for
chain functors.